3x^2-12x-7=0

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Solution for 3x^2-12x-7=0 equation: 


Simplifying
3x2 + -12x + -7 = 0

Reorder the terms:
-7 + -12x + 3x2 = 0

Solving
-7 + -12x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-2.333333333 + -4x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -4x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -4x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + 2.333333333
-4x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-4x + x2 = 2.333333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 2.333333333 + 4

Reorder the terms:
4 + -4x + x2 = 2.333333333 + 4

Combine like terms: 2.333333333 + 4 = 6.333333333
4 + -4x + x2 = 6.333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 6.333333333

Calculate the square root of the right side: 2.516611478

Break this problem into two subproblems by setting 
(x + -2) equal to 2.516611478 and -2.516611478.


Subproblem 1
x + -2 = 2.516611478

Simplifying
x + -2 = 2.516611478

Reorder the terms:
-2 + x = 2.516611478

Solving
-2 + x = 2.516611478

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 2.516611478 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.516611478 + 2
x = 2.516611478 + 2

Combine like terms: 2.516611478 + 2 = 4.516611478
x = 4.516611478

Simplifying
x = 4.516611478


Subproblem 2
x + -2 = -2.516611478

Simplifying
x + -2 = -2.516611478

Reorder the terms:
-2 + x = -2.516611478

Solving
-2 + x = -2.516611478

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = -2.516611478 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.516611478 + 2
x = -2.516611478 + 2

Combine like terms: -2.516611478 + 2 = -0.516611478
x = -0.516611478

Simplifying
x = -0.516611478


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.516611478, -0.516611478}

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